Year: 2021
Type: preprint
Abstract: In this paper we investigate iteration of maps on lattices and the corresponding polynomial-like iterative equation. Since a lattice need not have a metric space structure, neither the Schauder fixed point theorem nor the Banach fixed point theorem is available. Using Tarski's fixed point theorem, we prove the existence of order-preserving solutions on convex complete sublattices of Riesz spaces. Further, in $\mathbb{R}^n$ and $\mathbb{R}$, special cases of Riesz space, we discuss upper semi-continuous solutions and integrable solutions respectively. Finally, we indicate more special cases of Riesz space for discussion on the iterative equation.
Source: arXiv (Cornell University)
Authors: Gopalakrishna, Chaitanya, Zhang, Weinian
Institutions: Indian Statistical Institute, Sichuan University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1059606634, G1623511854, G565510363
OpenAlex ID: W3162880828